SIC-POVMs and Lie Algebras
ORAL
Abstract
A symmetric informationally complete positive operator valued measure (SIC-POVM) is usually thought of as a highly symmetric structure in quantum state space. However Appleby, Flammia and Fuchs (J. Math. Phys. \textbf{52}, 022202, 2011) have shown that the existence of a SIC-POVM in dimension $d$ is equivalent to a proposition concerning the Lie Algebra $\mathrm{gl}(d,C)$. Related to this they show that there is, associated to each SIC-POVM, a rich and intricate geometric structure in the adjoint representation space of $\mathrm{gl}(d,C)$. In this talk we present a deeper exploration of this structure.
*This work was supported in part by the U. S. Office of Naval Research (Grant No. N00014-09-1-0247) and by the Natural Sciences and Engineering Research Council of Canada.
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